"From a distance they look like sheet music, fat little blobs on rows of horizontal lines. There seem to be special places they like to perch, and it’s not at all clear to me why, but one thing stands out. If a lot of birds are perching on a wire, they end up evenly spaced.

"That’s a mathematical pattern, and I think there’s a mathematical explanation. I don’t think the birds 'know' they ought to space themselves out evenly. But each bird has its own 'personal space,' and if another bird gets too close, it will sidle along the wire to leave a bit more room, unless there’s another bird crowding it from the other side.

"When there are just a few birds, they end up randomly spaced. But when there are a lot, they get pushed close together. As each one sidles along to make itself feel more comfortable, the 'population pressure' evens them out. Birds at the edge of denser regions get pushed into less densely populated regions. And since the birds are all of the same species (usually they’re pigeons), they all have much the same idea of what their personal space should be. So they space themselves evenly.

"Not exactly evenly, of course. That would be a Platonic ideal. As such, it helps us to comprehend a more messy reality.

"You could do the math on this problem if you wanted to. Write down some simple rules for how birds move when the neighbors get too close, plonk them down at random, run the rules, and watch the spacing evolve. But there’s an analogy with a common physical system, where that math has already been done, and the analogy tells you what to expect.

"It’s a bird crystal.

"The same process that makes birds space themselves regularly makes the atoms in a solid object line up to form a repetitive lattice. The atoms also have a 'personal space': they repel each other if they’re too close together. In a solid, the atoms are forced to pack fairly tightly, but as they adjust their personal spaces, they arrange themselves in an elegant crystal lattice.

"The bird lattice is one-dimensional, since they’re sitting on a wire. A one-dimensional lattice consists of equally spaced points. When there are just a few birds, arranged at random and not subject to population pressure, it’s not a crystal, it’s a gas.

"This isn’t just a vague analogy. The same mathematical process that creates a regular crystal of salt or calcite also creates my 'bird crystal.'"

58 comments:

Do you know, until I read this, I just took it for granted that birds lined themselves up relatively equally on a phone wire. I didn't realise there was an actual mathematical equation to it...amazing, yet it's one of those things we see all the time and never think about.

I love the photograph of the birds on the line. Works so well for this theme and I find the spacing interesting. When I used to feed birds on my deck wall ledge (still do in particularly bad weather), I notice that they have there own space even when relatively close together. Different from a line but I guess the same principle. I hope you have a pleasant weekend.

What I have observed recently about pigeons on a phone wire is that they are bunched together on each side of the pole. I figure that they don't sit in the center because of the droop--the wire more stable and less wobbly closer to the pole. And close together because--it's COLD out there!

I love this photo! It reminds me of the animated film Monsters where at the beginning of the film, it shows some birds on a line. And when a huge ugly bird joined them, they boycott it. They got hurt when they tried to harm the ugly bird. A funny cartoon.

I was just about to comment about species of sparrows when I though I'd look to see what I had said last week about woodpeckers and nuthatches, only to find I've commented on the wrong post, the wrong blog, or messed it up altogether! Never mind, I love the picture, especially end on:)

Wow, what awesome photos you take!!! I just visited your other blog (all photos of birds mostly) and was quite impressed. We are studying birds in school (homeschool) and I'm going to show the kids your site. Love the LONG photo hunt picture as well!Have a great day,Elinor

Got your comment on my blog, and this is TOO funny. I always wondered why the birds kind of knew exactly what to do on the wire. They all sit like they have a perfect spot, and exactly in an even spaced row! Birds must be mathematical geniuses! --JB

Hi there, your post been recommended by JB since I saw his arrangement of birds. I think we under-estimate birds, they are in fact intelligent creatures. However, I was thinking, may be they arrange themselves in the patterns or spaced equally, because they know how much space they need to take off. Anyway, this is very interesting, I started some bird watching this year, so I will consider this into my observations. Nice blog you have too. Anna :)